It follows from Assumption REF  that the set of fixed points \(C\)  contains a \(k-\) dimensional submanifold \(S\) . In order that this submanifold \(S\)  itself has a level set representation, we impose an algebraic assumption on the existence of a suitable factorisation of \(h(z)\) . Such assumptions are also made in the ODE setting in [1]}.
